Teach Yourself Series: 20 Age Problems and Solutions in Algebra

Algebra

Use my detailed solutions to the 20 Algebra questions below to learn the fundamentals of Algebra.

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1.     A boy is 10 years older than his brother. In 4 years he will be twice as old as his brother. Find the present age of each.

2.     A father is 4 times as old as his son. In 20 years the father will be twice as old as his son. Find the present age of each.

3.     Pat is 20 years older than his son James. In two years Pat will be twice as old as James. How old are they now?

4.     Fred is 4 years older than Barney. Five years ago the sum of their ages was 48. How old are they now?

5.     John is four times as old as Martha. Five years ago the sum of their ages was 50. How old are they now?

6.     Tim is 5 years older than JoAnn. Six years from now the sum of their ages will be 79. How old are they now?

7.     Jack is twice as old as Lacy. In three years the sum of their ages will be 54. How old are they now?

8.     The sum of the ages of John and Mary is 32. Four years ago, John was twice as old as Mary. Find the present age of each.

9.     The sum of the ages of a father and son is 56. Four years ago the father was 3 times as old as the son. Find the present age of each.

10.  The sum of the ages of a wood plaque and a bronze plaque is 20 years. Four years ago, the bronze plaque was one-half the age of the wood plaque. Find the present age of each plaque.

11.  A is now 34 years old, and B is 4 years old. In how many years will A be twice as old as B?

12.  A man’s age is 36 and that of his daughter is 3 years. In how many years will the man be 4 times as old as his daughter?

13.  An Oriental rug is 52 years old and a Persian rug is 16 years old. How many years ago was the Oriental rug four times as old as the Persian Rug?

14.  The age of the older of two boys is twice that of the younger; 5 years ago it was three times that of the younger. Find the age of each.

15.  A pitcher is 30 years old, and a vase is 22 years old. How many years ago was the pitcher twice as old as the vase?

16.  Marge is twice as old as Consuelo. The sum of their ages seven years ago was 14 years. How old are they now?

17.  The sum of Jason and Mandy’s age is 35. Ten years ago Jason was double Mandy’s age. How old are they now?

18.  A limestone statue is 56 years older than a marble statue. In 12 years, the limestone will be three times as old as the marble statue. Find the present age of the statues.

19.  Brandon is 9 years older than Ronda. In four years the sum of their ages will be 91. How old are they now?

20.  A father is three times as old as his son, and his daughter is 3 years younger than the son. If the sum of their ages 3 years ago was 63 years, find the present age of the father.